The local policy \(\pi _L\)  navigates the agent to the long-term goal sampled by the potential function network. It uses the Fast Marching Method [1]} to compute the shortest path from the current location \(p_t\)  to the long-term goal \(g_t\)  using the obstacle channel from the semantic map \(m_t\) . The local policy then takes deterministic actions to navigate the agent along this shortest path. This was found to be as effective as a learned local policy in prior work [2]}, [3]}.
